X998

ISOGONAL CONJUGATE OF X997

X998 is the isogonal conjugate of X997.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 46, 58 }: Central Line L(46, 58) { 6, 517 }: Central Line L(6, 517) { 106, 614 }: Central Line L(106, 614) { 1, 908 }: Central Line L(1, 908) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_997 = MIDPOINT OF X(1) AND X(200) (0.5053, 0.1685) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_1 = INCENTER (0.5714, 0.2333) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_998 = ISOGONAL CONJUGATE OF X(997) (0.6186, 0.3014) A B C X997 X46 X58 X6 X517 X106 X614 X1 X908 X998 (a, b, c) = (5, 6, 7) | AB = 1

X998 (ISOGONAL CONJUGATE OF X997) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/[a^{3} - a^{2}(b + c) - a(b - c)^{2} + (b + c)(b^{2} + c^{2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.669294774495\)
▸ Incident Central Lines4 lines

{1, 908}, {6, 517}, {46, 58}, {106, 614}

▸ Functional Relations1 relation